Love the cow/milk analogy!
I began my design career in my late 30s, before the web, and when typically, a designer only had access to Photoshop, Illustrator, etc on their work desktop Mac. (Yes, those days without laptops or tablets existed!). My first job was with a tiny studio that emphasized starting with sketches in a sketchbook, and I have maintained that habit over 30+ years in design. Even when attending meetings, when everyone else is taking notes on their laptop, I take notes by hand. I remember better, and — at least for me — I’m more able to listen and take notes by hand than listen and type. Typing seems to draw all of my mental resources and I miss hearing nuances of the spoken word.
A former coworker got me on to Cambridge grid-lined spiral notebooks (yellow pages, drop-out blue grid) and the use of a Frixion pen. These are my “modern” accommodations to starting with hand-written notes and sketches to think through user flows, site architecture, and the like.